As a method for measuring a profile of a mirror with precision in the order of nanometer, there are generally used a method (Long Trace Profiler) for obtaining profile data by measuring normal vectors to a mirror surface at a predetermined interval and integrating the measurement data, and a method using an interferometer. The former method (see patent document 1) for measuring normal vectors comprises: measuring normal vectors at multitude points on a surface of a measurement object; calculating tilt angles of the respective measurement points with respect to a reference line; and interpolating data between the adjoining measurement points to obtain a profile of the measurement object. In the above method, it is necessary to reduce the interval between the measurement points in order to measure the profile of the measurement object with high precision. Accordingly, a large number of measurement points is required to measure a profile of a measurement object having a large area, which may increase a time required for measurement. In the latter method (see patent document 2) using an interferometer, the size of a measurement aperture is limited. Accordingly, in the case where a profile of a measurement object having a larger size than the size of the measurement aperture is to be measured, there is used a method comprising: measuring individual areas in a manner that the adjoining measurement areas are overlapped with use of an XY-stage as a mirror stage; and after the measurement is terminated, stitching pieces of data in such a manner an overlapping error on the overlapping area is minimized to obtain the overall profile of the measurement object.
In the method using the overlapping area, precision on measurement data is determined by angle accuracy at the time of stitching. In performing measurement using an interferometer, measurement with precision as high as the order of nanometer or higher is possible, if the measurement is performed in a null fringe condition. A flat reference surface capable of measuring a profile of a measurement object with precision as high as 1 nm order or less is used as a reference plane in the measurement using an interferometer by performing a three-plane matching method or a like method in advance. However, in the case where a profile of a measurement object is not measurable in a null fringe condition, a measurement error corresponding to a fringe may be generated in the measurement data. The measurement error may make it impossible to accurately calculate stitching angles between the adjoining pieces of data at the time of stitching. Since the error is integrated each time the stitching is performed, the measurement error may greatly affect the process of acquiring the overall profile of the measurement object.
In view of the above, in the case where stitching measurement using an interferometer is performed, it is required to obtain accurate stitching angles. In view of the above, patent document 3 discloses a method comprising: measuring angles of a mirror in different postures with high precision separately at the time of measuring pieces of data; and stitching the pieces of data by using the posture angles of the mirror. In the case where stitching measurement is performed, it is required to maintain positional relations between a reference plane of the interferometer and a sample stage. Accordingly, in the method of patent document 3, stability of ambient temperature and measurement precision on angles are the keys to secure profile precision. The measurement method recited in patent document 3 is suitable as a method for measuring a surface profile of a measurement object having a large area such as a glass substrate to be used in a liquid crystal display panel in the order of sub micron, but is not suitable as a method for measuring a profile of a measurement object with ultra precision corresponding to nano order or sub-nano order. The absolute precision of a linear encoder currently available on the market with a highest precision is at most about 5×10−8 rad. There is a demand for a method for obtaining stitching angles with higher precision in the order of nanometer to attain precision with respect to the entirety of measurement data.
The inventors of the present application have proposed a system, in non-patent document 1, for measuring a profile of an X-ray mirror in the entirety of a space wavelength region with high precision and measurement reproducibility of 1 nm order or less in PV (peak-to-valley) value. The measurement principle of non-patent document 1 is based on profile measurement by stitching with use of a Michelson microscopic interferometer having a possibility of high space resolution, and is directed to correct stitching errors by using data from a Fizeau interferometer capable of high precision measurement in a space wavelength region corresponding to an intermediate/long cycle. In the stitching, tilts between adjoining pieces of measurement data are optimally corrected by utilizing a matching degree on overlapping areas which are measured in common with respect to the pieces of profile measurement data on the adjoining areas. In performing the stitching, even if there is a profile error as small as 0.1 nm order, which may be generated from a slight profile error on the reference plane, a focus distance difference, or a like factor, an error in a long cycle component may be generated in the overall profile data obtained after the stitching. In view of the above, in the measurement system recited in non-patent document 1, an error in focus distance of the Michelson microscopic interferometer is suppressed to 0.3 μm or less to suppress a variation in angle error, which may be generated in stitching adjoining pieces of profile data due to a measurement error included in profile measurement data corresponding to each one shot, to 1×10−7 rad or less; and a zone for evaluating the overlapping areas is optimized. Thus, there is established an optimum correcting method using a Fizeau interferometer, in which performances of the two measuring devices are maximally shown.
A profile measurement was performed by using the measurement system recited in non-patent document 1, and a plane mirror and an elliptical mirror were produced by numerically-controlled PCVM (Plasma chemical vaporization matching), and EEM (Elastic emission matching). The plane mirror was evaluated by using X-rays of 0.06 nm wavelength at 1 km beam line of SPring-8. As a result of the evaluation, it was confirmed that the plane mirror had a sufficiently uniform reflection intensity distribution with respect to reflection X-rays. Also, it was confirmed that the condensing mirror of an elliptical shape had a property of condensing beams of diffraction limit at the same beam line. It was also confirmed that the half bandwidth of the intensity profile on condensing beams that has been designed and measured was 180 nm, and that the profile was substantially equivalent to a profile presumably obtained based on Fresnel-Kirchhoff diffraction integral considering a surface profile.
To obtain condensing beams of a smaller size, it is required to design and fabricate an elliptical mirror having a larger incident angle and a steeper profile, in other words, a larger numerical aperture. There has been designed a condensing mirror of an elliptical shape having a property that the half bandwidth of an intensity profile with respect to condensing beams of diffraction limit is about 30 nm. However, it is impossible to collectively measure the curved surface of the elliptical mirror with a Fizeau interferometer. In performing measurement using the Fizeau interferometer, if the angle defined by a surface of the reference plane and a surface of the measurement object exceeds 1×10−4 rad, the fringe pattern has a high density, which may make it impossible to acquire surface profile data. The measurement method recited in non-patent document 1 is proposed based on the premise that the entirety of a targeted area of a measurement surface can be collectively measured with the Fizeau interferometer. Accordingly, in the measurement method recited in non-patent document 1, it is impossible to measure the entire surface of a measurement object having such a steep profile that the angle defined by the reference plane of the Fizeau interferometer and the measurement surface exceeds 1×10−4 rad.    Patent document 1: Japanese Patent No. 3,598,983    Patent document 2: Japanese Patent No. 2,531,596    Patent document 3: Japanese Patent No. 3,562,338Non-patent document 1: Development of Profile Measurement System Utilizing Interferometer for High-precision X-ray mirror, by Kazuto Yamauchi, Kazuya Yamamura, Hidekazu Mimura, Yasuhisa Sano, Akihisa Kubota, Yasuhiro Sekito, Kazumasa Ueno, Alexei Souvorov, Kenji Tamasaku, Makina Yahashi, Tetsuya Ishikawa, and Yuzo Mori, Journal of Japan Society for Precision Engineering, 69(2003)856.